A quality control engineer intends to use the mean of a random sample of $n=85$ to estimate the average time it takes to manufacture an item. If, based on experience, the engineer can assume that $\sigma=4.8$ hours for such data, what can he assert with probability 0.99 about the maximum error of the estimate?
A) $E \approx 1.34$ hours
B) $E \approx 0.13$ hours
C) $E \approx 0.15$ hours
D) $E \approx 1.21$ hours

Question

Quizplus · Accepted Answer

The maximum error of the estimate (E) can be calculated using the formula for the margin of error in estimating a population mean: $E = Z \cdot \frac{\sigma}{\sqrt{n}}$, where $Z$ is the Z-score corresponding to the desired confidence level (0.99 in this case), $\sigma$ is the population standard deviation, and $n$ is the sample size. For a 0.99 confidence level, the Z-score is approximately 2.576. Plugging in the given values: $E = 2.576 \cdot \frac{4.8}{\sqrt{85}} \approx 1.34$ hours.

A Quality Control Engineer Intends to Use the Mean of a Random